- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / csup / csup_csup.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/csup/csup_csup.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/csup/csup_csup.etc
new file mode 100644 (file)
index 0000000..661d896
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/csup/csup_csup.etc
@@ -0,0 +1,33 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/substitution/ldrop_ldrop.ma".
+include "basic_2/substitution/csup.ma".
+
+(* SUPCLOSURE ***************************************************************)
+
+(* Main forward lemmas ******************************************************)
+
+theorem csup_trans_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ > ⦃L0, T2⦄ →
+                             ∀T3. ⦃L0, T2⦄ > ⦃L, T3⦄ →
+                             L = L0 ∨ ⦃L, T1⦄ > ⦃L, T3⦄.
+#L #L0 #T1 #T2 * -L -L0 -T1 -T2 /2 width=1/
+[ #I #L0 #K0 #V0 #i #HLK0 #T3 #H
+  lapply (ldrop_pair2_fwd_cw … HLK0 T3) -HLK0 #H1
+  lapply (csup_fwd_cw … H) -H #H2
+  lapply (transitive_lt … H1 H2) -H1 -H2 #H
+  elim (lt_refl_false … H)
+| #a #I #L0 #V2 #T2 #T3 #HT23
+  elim (csup_inv_ldrop … HT23 I V2 0 ?) -HT23 // #H1 #H2 destruct /2 width=1/
+  qed-.